Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.

Empty-nest elderly:mahjong and Chinese square dance for improving the cognitive function in the community

Objective: The elderly population has proliferated worldwide. The empty-nest family pattern has become predominant among the aging people, and they are more vulnerable to the development of cognitive disorders. However, there is no standardized service in the community nursing care that includes procedures on how to improve the cognitive function of the elderly. Meanwhile, the booming number of empty-nest elderly stimulates the community nurses to assume the responsibility for their care. All of these bring more difficulties and opportunities for community nurses who are dedicated to the prevention of geriatric cognitive disorders.Methods: The authors reviewed the literature related to "empty-nest elderly", "cognitive function","mahjong",and "Chinese square dance" in the Elsevier, Web of Science(WOS), China National Knowledge Infrastructure(CNKI), Springer and PubMed databases. The study illustrates the utility possibility of an efficient and straightforward method for improving the cognitive function among the elderly in the context of community nursing care in China and even in the rest of the world.Results: Mental and physical activity contributes to cognitive fitness and may be beneficial in delaying cognitive decline. Mental activities, such as playing mahjong, and physical activities, such as the Chinese square dance, are common Chinese activities. Both of them can affect cognitive function in some way.Conclusions: China is experiencing one of its most severe aging problems. Community health personnel and related professionals may consider using mahjong and Chinese square dance to promote psychological health in empty-nest elderly individuals in the community.

BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.

Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.

Regional Logistics Demand Forecast Based on Least Square and Radial Basis Function

Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies.It has the characteristics of a small amount of data and being nonlinear,so the traditional prediction method can not guarantee the accuracy of prediction.Taking Xiamen City as an example,this paper selects the primary industry,the secondary industry,the tertiary industry,the total amount of investment in fixed assets,total import and export volume,per capita consumption expenditure,and the total retail sales of social consumer goods as the influencing factors,and uses a combining model least square and radial basis function(LS-RBF)neural network to analyze the related data from years 2000 to 2019,so as to predict the logistics demand from years 2020 to 2024.The model can well fit the training data,and the experimental results obtained from the comparison between the predicted value and the actual value in 2019 show that the error rate is very small.Therefore,the prediction results are reasonable and reliable.This method has high prediction accuracy,and it is suitable for irregular regional logistics demand forecast.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Mean-square Almost Periodic Random Functions

In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.

SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS

In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.

基于SIMD的Square Root函数高性能实现与优化

在计算机图形学、积分计算和神经网络等应用场景中,平方根函数的高性能实现在构建处理器的基础软件生态中起到了十分重要的作用。随着ARM架构处理器得到广泛的使用,研究ARM架构下的函数快速算法实现变得更加关键。当前大量处理器都采用了SIMD架构,所以,研究基于SIMD实现高性能函数计算方法具有重要的研究意义和发展前景。因此,对平方根函数进行了高性能的实现与优化。通过分析IEEE 754标准的浮点数在内存中的存储格式,设计了高效的平方根函数算法;然后通过结合平方根倒数和泰勒公式算法,进一步提高了算法精度;最后通过SIMD优化进一步提升了算法性能。实验结果表明,在满足精度的前提下,相比于libm算法库,实现的平方根函数的,性能提高了约7倍,相比于ARM V8提供的计算平方根的指令在性能上提高了约3倍。

Temperature prediction control based on least squares support vector machines

A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.

Riemann Boundary Value Problem with Square Roots on an Open Arc

The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.

New predictive control algorithms based on Least Squares Support Vector Machines

Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlinear system, the system model is built by using LS-SVM with linear kernel function, and then the obtained linear LS-SVM model is transformed into linear input-output relation of the controlled system. However, for the strongly nonlinear system, the off-line model of the controlled system is built by using LS-SVM with Radial Basis Function (RBF) kernel. The obtained nonlinear LS-SVM model is linearized at each sampling instant of system running, after which the on-line linear input-output model of the system is built. Based on the obtained linear input-output model, the Generalized Predictive Control (GPC) algorithm is employed to implement predictive control for the controlled plant in both algorithms. The simulation results after the presented algorithms were implemented in two different industrial processes model; respectively revealed the effectiveness and merit of both algorithms.

Generalizations of Hermite-Hadamard Type Inequalities Involving S-convex Functions

Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.

Estimation under a Finite Mixture of Exponentiated Exponential Components Model and Balanced Square Error Loss

By exponentiating each of the components of a finite mixture of two exponential components model by a positive parameter, several shapes of hazard rate functions are obtained. Maximum likelihood and Bayes methods, based on square error loss function and objective prior, are used to obtain estimators based on balanced square error loss function for the parameters, survival and hazard rate functions of a mixture of two exponentiated exponential components model. Approximate interval estimators of the parameters of the model are obtained.

Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

The Weibull distribution is regarded as among the finest in the family of failure distributions.One of the most commonly used parameters of the Weibull distribution(WD)is the ordinary least squares(OLS)technique,which is useful in reliability and lifetime modeling.In this study,we propose an approach based on the ordinary least squares and the multilayer perceptron(MLP)neural network called the OLSMLP that is based on the resilience of the OLS method.The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers,and eases the difficulty of determining weights in case of the weighted least square(WLS).Another method is proposed by incorporating a weight into the general entropy(GE)loss function to estimate the parameters of the WD to obtain a modified loss function(WGE).Furthermore,a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation(BLWGE)by using a weighted GE loss function.The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes.In addition,the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods,in terms of the mean squared error and requirements related to time.

Application of least squares vector machines in modelling water vapor and carbon dioxide fluxes over a cropland

Least squares support vector machines (LS-SVMs), a nonlinear kemel based machine was introduced to investigate the prospects of application of this approach in modelling water vapor and carbon dioxide fluxes above a summer maize field using the dataset obtained in the North China Plain with eddy covariance technique. The performances of the LS-SVMs were compared to the corresponding models obtained with radial basis function (RBF) neural networks. The results indicated the trained LS-SVMs with a radial basis function kernel had satisfactory performance in modelling surface fluxes; its excellent approximation and generalization property shed new light on the study on complex processes in ecosystem.

Least squares weighted twin support vector machines with local information

A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.